96 Colours and their Relations. [January, 



the above series, and the resulting values of the reciprocals 

 of the wave-lengths for the mean colours will stand thus : — 



Red. Orange. Yellow. Green. Blue. Indigo. Violet. 

 1463-676, 1626-307, 1788-937, 1951-568, 2114-198, 2276-829, 2439-460, 



forming an arithmetical progression, of which the common 

 difference is 162*631. 



From the above, result the following numbers for the 

 borders of the colours : — 

 1382-360, 1544-991, 1707-622, 1870-252, 2032-883, 2195-513, 2358-144, 2520-775, 



— an arithmetical progression, of which the common dif- 

 ference is also 162*631. 



From this last series we obtain the wave-lengths of the 

 borders of the colours, in order to compare them with the 

 wave-lengths given by Listing from observation. The fol- 

 lowing table gives the result ; — 



Observed. 



Calculated. 



Differences 4- 



Differences — 



7234 



6472 

 5856 



5347 



7234*09 

 6472*529 

 5856-I 

 5346*873 



0*09 



0-529 



0*1 



OT27 



4919 



4919-121 



0"I2I 





4555 

 4241 



3967 



4554744 

 4240-624 



3967*034 



0*034 



0-256 

 0-376 



0-874 0-759 



These small differences are considerably within the limits 

 of probable errors of observation, the more especially as 

 Listing's numbers do not extend beyond four figures. It 

 may accordingly be fairly concluded that, when reduced to 

 their simplest form, by making the lowest number unity, the 

 series will be for the borders of the colours — 1, 1*117647, 

 i*235295> 1*352942, 1-470589, 1*588236, 1*705883, 1*832530; 

 and for the mean rays of the colours — 



Red. Orange. Yellow. Green. Blue. Indigo. Violet. 



i, i-ii', i*22', 1-33', 1*44', 1*55', i-66' 



On comparing these two series with the three musical 

 scales, it will be perceived that with these the first series 

 has no points of correspondence whatever. Neither has the 

 second series with the ideal musical scale. But in the two 

 others the green corresponds exactly with the fa, while the 

 violet tallies also with the la of the harmonic scale only. 

 Moreover, if the violet be divided by the orange, the quotient, 



